Keyboard shortcuts

Press ← or → to navigate between chapters

Press ? to show this help

Press Esc to hide this help

BinaryLaurentEvaluation

Abstract

Complete binary Laurent evaluation

Definition 1.1 (ABField).

Lean statement: D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.ABField

Formalization. D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.ABField (✓ std3).

Source. Repository-derived.

Acknowledgement. Bojko Bakalov and Victor G. Kac (2004). Twisted Modules over Lattice Vertex Algebras. DOI: 10.1142/9789812702562_0001. URL: https://arxiv.org/abs/math/0402315v1.

Commentary.

The two ordered Hahn coefficients are subtracted before support or evaluation. All numerator and diagonal exponents are signed. The signed kernel identity and complete residue calculation include positive-power cancellation and zero or empty degree fibers. The original contextual coefficient API is reused after its separate visibility publication. The original AB coefficient-field carriers and the three consumed ABOuterTaylor algebra helpers are kept here under their original declaration namespaces, without the unconsumed AB residue or middle-proof chains.

Definition 1.2 (y).

Lean statement: D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.y

Formalization. D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.y (✓ std3).

Source. Repository-derived.

Acknowledgement. Bojko Bakalov and Victor G. Kac (2004). Twisted Modules over Lattice Vertex Algebras. DOI: 10.1142/9789812702562_0001. URL: https://arxiv.org/abs/math/0402315v1.

Commentary.

The two ordered Hahn coefficients are subtracted before support or evaluation. All numerator and diagonal exponents are signed. The signed kernel identity and complete residue calculation include positive-power cancellation and zero or empty degree fibers. The original contextual coefficient API is reused after its separate visibility publication. The original AB coefficient-field carriers and the three consumed ABOuterTaylor algebra helpers are kept here under their original declaration namespaces, without the unconsumed AB residue or middle-proof chains.

Definition 1.3 (z).

Lean statement: D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.z

Formalization. D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.z (✓ std3).

Source. Repository-derived.

Acknowledgement. Bojko Bakalov and Victor G. Kac (2004). Twisted Modules over Lattice Vertex Algebras. DOI: 10.1142/9789812702562_0001. URL: https://arxiv.org/abs/math/0402315v1.

Commentary.

The two ordered Hahn coefficients are subtracted before support or evaluation. All numerator and diagonal exponents are signed. The signed kernel identity and complete residue calculation include positive-power cancellation and zero or empty degree fibers. The original contextual coefficient API is reused after its separate visibility publication. The original AB coefficient-field carriers and the three consumed ABOuterTaylor algebra helpers are kept here under their original declaration namespaces, without the unconsumed AB residue or middle-proof chains.

Definition 1.4 (originalRational).

Lean statement: D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.originalRational

Formalization. D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.originalRational (✓ std3).

Source. Repository-derived.

Acknowledgement. Bojko Bakalov and Victor G. Kac (2004). Twisted Modules over Lattice Vertex Algebras. DOI: 10.1142/9789812702562_0001. URL: https://arxiv.org/abs/math/0402315v1.

Commentary.

The two ordered Hahn coefficients are subtracted before support or evaluation. All numerator and diagonal exponents are signed. The signed kernel identity and complete residue calculation include positive-power cancellation and zero or empty degree fibers. The original contextual coefficient API is reused after its separate visibility publication. The original AB coefficient-field carriers and the three consumed ABOuterTaylor algebra helpers are kept here under their original declaration namespaces, without the unconsumed AB residue or middle-proof chains.

Theorem 1.5 (coefficient_scalar).

Lean statement: D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.coefficient_scalar

Proof. Machine-checked in Lean as D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.coefficient_scalar (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. Bojko Bakalov and Victor G. Kac (2004). Twisted Modules over Lattice Vertex Algebras. DOI: 10.1142/9789812702562_0001. URL: https://arxiv.org/abs/math/0402315v1.

Commentary.

The two ordered Hahn coefficients are subtracted before support or evaluation. All numerator and diagonal exponents are signed. The signed kernel identity and complete residue calculation include positive-power cancellation and zero or empty degree fibers. The original contextual coefficient API is reused after its separate visibility publication. The original AB coefficient-field carriers and the three consumed ABOuterTaylor algebra helpers are kept here under their original declaration namespaces, without the unconsumed AB residue or middle-proof chains.

Theorem 1.6 (binary_kernel_coeff).

Lean statement: D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.binary_kernel_coeff

Proof. Machine-checked in Lean as D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.binary_kernel_coeff (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. Bojko Bakalov and Victor G. Kac (2004). Twisted Modules over Lattice Vertex Algebras. DOI: 10.1142/9789812702562_0001. URL: https://arxiv.org/abs/math/0402315v1.

Commentary.

The two ordered Hahn coefficients are subtracted before support or evaluation. All numerator and diagonal exponents are signed. The signed kernel identity and complete residue calculation include positive-power cancellation and zero or empty degree fibers. The original contextual coefficient API is reused after its separate visibility publication. The original AB coefficient-field carriers and the three consumed ABOuterTaylor algebra helpers are kept here under their original declaration namespaces, without the unconsumed AB residue or middle-proof chains.

Theorem 1.7 (signed_kernel_choose).

Lean statement: D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.signed_kernel_choose

Proof. Machine-checked in Lean as D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.signed_kernel_choose (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. Bojko Bakalov and Victor G. Kac (2004). Twisted Modules over Lattice Vertex Algebras. DOI: 10.1142/9789812702562_0001. URL: https://arxiv.org/abs/math/0402315v1.

Commentary.

The two ordered Hahn coefficients are subtracted before support or evaluation. All numerator and diagonal exponents are signed. The signed kernel identity and complete residue calculation include positive-power cancellation and zero or empty degree fibers. The original contextual coefficient API is reused after its separate visibility publication. The original AB coefficient-field carriers and the three consumed ABOuterTaylor algebra helpers are kept here under their original declaration namespaces, without the unconsumed AB residue or middle-proof chains.

Definition 1.8 (BinaryPolynomial).

Lean statement: D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.BinaryPolynomial

Formalization. D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.BinaryPolynomial (✓ std3).

Source. Repository-derived.

Acknowledgement. Bojko Bakalov and Victor G. Kac (2004). Twisted Modules over Lattice Vertex Algebras. DOI: 10.1142/9789812702562_0001. URL: https://arxiv.org/abs/math/0402315v1.

Commentary.

The two ordered Hahn coefficients are subtracted before support or evaluation. All numerator and diagonal exponents are signed. The signed kernel identity and complete residue calculation include positive-power cancellation and zero or empty degree fibers. The original contextual coefficient API is reused after its separate visibility publication. The original AB coefficient-field carriers and the three consumed ABOuterTaylor algebra helpers are kept here under their original declaration namespaces, without the unconsumed AB residue or middle-proof chains.

Definition 1.9 (BinaryExponent).

Lean statement: D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.BinaryExponent

Formalization. D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.BinaryExponent (✓ std3).

Source. Repository-derived.

Acknowledgement. Bojko Bakalov and Victor G. Kac (2004). Twisted Modules over Lattice Vertex Algebras. DOI: 10.1142/9789812702562_0001. URL: https://arxiv.org/abs/math/0402315v1.

Commentary.

The two ordered Hahn coefficients are subtracted before support or evaluation. All numerator and diagonal exponents are signed. The signed kernel identity and complete residue calculation include positive-power cancellation and zero or empty degree fibers. The original contextual coefficient API is reused after its separate visibility publication. The original AB coefficient-field carriers and the three consumed ABOuterTaylor algebra helpers are kept here under their original declaration namespaces, without the unconsumed AB residue or middle-proof chains.

Definition 1.10 (binaryRational).

Lean statement: D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.binaryRational

Formalization. D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.binaryRational (✓ std3).

Source. Repository-derived.

Acknowledgement. Bojko Bakalov and Victor G. Kac (2004). Twisted Modules over Lattice Vertex Algebras. DOI: 10.1142/9789812702562_0001. URL: https://arxiv.org/abs/math/0402315v1.

Commentary.

The two ordered Hahn coefficients are subtracted before support or evaluation. All numerator and diagonal exponents are signed. The signed kernel identity and complete residue calculation include positive-power cancellation and zero or empty degree fibers. The original contextual coefficient API is reused after its separate visibility publication. The original AB coefficient-field carriers and the three consumed ABOuterTaylor algebra helpers are kept here under their original declaration namespaces, without the unconsumed AB residue or middle-proof chains.

Definition 1.11 (binaryExpansion).

Lean statement: D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.binaryExpansion

Formalization. D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.binaryExpansion (✓ std3).

Source. Repository-derived.

Acknowledgement. Bojko Bakalov and Victor G. Kac (2004). Twisted Modules over Lattice Vertex Algebras. DOI: 10.1142/9789812702562_0001. URL: https://arxiv.org/abs/math/0402315v1.

Commentary.

The two ordered Hahn coefficients are subtracted before support or evaluation. All numerator and diagonal exponents are signed. The signed kernel identity and complete residue calculation include positive-power cancellation and zero or empty degree fibers. The original contextual coefficient API is reused after its separate visibility publication. The original AB coefficient-field carriers and the three consumed ABOuterTaylor algebra helpers are kept here under their original declaration namespaces, without the unconsumed AB residue or middle-proof chains.

Definition 1.12 (binaryModes).

Lean statement: D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.binaryModes

Formalization. D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.binaryModes (✓ std3).

Source. Repository-derived.

Acknowledgement. Bojko Bakalov and Victor G. Kac (2004). Twisted Modules over Lattice Vertex Algebras. DOI: 10.1142/9789812702562_0001. URL: https://arxiv.org/abs/math/0402315v1.

Commentary.

The two ordered Hahn coefficients are subtracted before support or evaluation. All numerator and diagonal exponents are signed. The signed kernel identity and complete residue calculation include positive-power cancellation and zero or empty degree fibers. The original contextual coefficient API is reused after its separate visibility publication. The original AB coefficient-field carriers and the three consumed ABOuterTaylor algebra helpers are kept here under their original declaration namespaces, without the unconsumed AB residue or middle-proof chains.

Definition 1.13 (binaryKernel).

Lean statement: D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.binaryKernel

Formalization. D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.binaryKernel (✓ std3).

Source. Repository-derived.

Acknowledgement. Bojko Bakalov and Victor G. Kac (2004). Twisted Modules over Lattice Vertex Algebras. DOI: 10.1142/9789812702562_0001. URL: https://arxiv.org/abs/math/0402315v1.

Commentary.

The two ordered Hahn coefficients are subtracted before support or evaluation. All numerator and diagonal exponents are signed. The signed kernel identity and complete residue calculation include positive-power cancellation and zero or empty degree fibers. The original contextual coefficient API is reused after its separate visibility publication. The original AB coefficient-field carriers and the three consumed ABOuterTaylor algebra helpers are kept here under their original declaration namespaces, without the unconsumed AB residue or middle-proof chains.

Theorem 1.14 (binary_laurent_jump).

Lean statement: D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.binary_laurent_jump

Proof. Machine-checked in Lean as D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.binary_laurent_jump (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. Bojko Bakalov and Victor G. Kac (2004). Twisted Modules over Lattice Vertex Algebras. DOI: 10.1142/9789812702562_0001. URL: https://arxiv.org/abs/math/0402315v1.

Commentary.

The two ordered Hahn coefficients are subtracted before support or evaluation. All numerator and diagonal exponents are signed. The signed kernel identity and complete residue calculation include positive-power cancellation and zero or empty degree fibers. The original contextual coefficient API is reused after its separate visibility publication. The original AB coefficient-field carriers and the three consumed ABOuterTaylor algebra helpers are kept here under their original declaration namespaces, without the unconsumed AB residue or middle-proof chains.

Theorem 1.15 (forward_readout).

Lean statement: D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.forward_readout

Proof. Machine-checked in Lean as D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.forward_readout (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. Bojko Bakalov and Victor G. Kac (2004). Twisted Modules over Lattice Vertex Algebras. DOI: 10.1142/9789812702562_0001. URL: https://arxiv.org/abs/math/0402315v1.

Commentary.

The two ordered Hahn coefficients are subtracted before support or evaluation. All numerator and diagonal exponents are signed. The signed kernel identity and complete residue calculation include positive-power cancellation and zero or empty degree fibers. The original contextual coefficient API is reused after its separate visibility publication. The original AB coefficient-field carriers and the three consumed ABOuterTaylor algebra helpers are kept here under their original declaration namespaces, without the unconsumed AB residue or middle-proof chains.

Theorem 1.16 (reverse_readout).

Lean statement: D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.reverse_readout

Proof. Machine-checked in Lean as D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.reverse_readout (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. Bojko Bakalov and Victor G. Kac (2004). Twisted Modules over Lattice Vertex Algebras. DOI: 10.1142/9789812702562_0001. URL: https://arxiv.org/abs/math/0402315v1.

Commentary.

The two ordered Hahn coefficients are subtracted before support or evaluation. All numerator and diagonal exponents are signed. The signed kernel identity and complete residue calculation include positive-power cancellation and zero or empty degree fibers. The original contextual coefficient API is reused after its separate visibility publication. The original AB coefficient-field carriers and the three consumed ABOuterTaylor algebra helpers are kept here under their original declaration namespaces, without the unconsumed AB residue or middle-proof chains.

Theorem 1.17 (binary_complete_residue).

Lean statement: D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.binary_complete_residue

Proof. Machine-checked in Lean as D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.binary_complete_residue (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. Bojko Bakalov and Victor G. Kac (2004). Twisted Modules over Lattice Vertex Algebras. DOI: 10.1142/9789812702562_0001. URL: https://arxiv.org/abs/math/0402315v1.

Commentary.

The two ordered Hahn coefficients are subtracted before support or evaluation. All numerator and diagonal exponents are signed. The signed kernel identity and complete residue calculation include positive-power cancellation and zero or empty degree fibers. The original contextual coefficient API is reused after its separate visibility publication. The original AB coefficient-field carriers and the three consumed ABOuterTaylor algebra helpers are kept here under their original declaration namespaces, without the unconsumed AB residue or middle-proof chains.

Definition 1.18 (binaryTaylor).

Lean statement: D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.binaryTaylor

Formalization. D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.binaryTaylor (✓ std3).

Source. Repository-derived.

Acknowledgement. Bojko Bakalov and Victor G. Kac (2004). Twisted Modules over Lattice Vertex Algebras. DOI: 10.1142/9789812702562_0001. URL: https://arxiv.org/abs/math/0402315v1.

Commentary.

The two ordered Hahn coefficients are subtracted before support or evaluation. All numerator and diagonal exponents are signed. The signed kernel identity and complete residue calculation include positive-power cancellation and zero or empty degree fibers. The original contextual coefficient API is reused after its separate visibility publication. The original AB coefficient-field carriers and the three consumed ABOuterTaylor algebra helpers are kept here under their original declaration namespaces, without the unconsumed AB residue or middle-proof chains.

Theorem 1.19 (binary_fractional_taylor).

Lean statement: D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.binary_fractional_taylor

Proof. Machine-checked in Lean as D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.binary_fractional_taylor (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. Bojko Bakalov and Victor G. Kac (2004). Twisted Modules over Lattice Vertex Algebras. DOI: 10.1142/9789812702562_0001. URL: https://arxiv.org/abs/math/0402315v1.

Commentary.

The two ordered Hahn coefficients are subtracted before support or evaluation. All numerator and diagonal exponents are signed. The signed kernel identity and complete residue calculation include positive-power cancellation and zero or empty degree fibers. The original contextual coefficient API is reused after its separate visibility publication. The original AB coefficient-field carriers and the three consumed ABOuterTaylor algebra helpers are kept here under their original declaration namespaces, without the unconsumed AB residue or middle-proof chains.

Theorem 1.20 (yz_ne_zero).

Lean statement: D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.yz_ne_zero

Proof. Machine-checked in Lean as D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.yz_ne_zero (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. Bojko Bakalov and Victor G. Kac (2004). Twisted Modules over Lattice Vertex Algebras. DOI: 10.1142/9789812702562_0001. URL: https://arxiv.org/abs/math/0402315v1.

Commentary.

The two ordered Hahn coefficients are subtracted before support or evaluation. All numerator and diagonal exponents are signed. The signed kernel identity and complete residue calculation include positive-power cancellation and zero or empty degree fibers. The original contextual coefficient API is reused after its separate visibility publication. The original AB coefficient-field carriers and the three consumed ABOuterTaylor algebra helpers are kept here under their original declaration namespaces, without the unconsumed AB residue or middle-proof chains.

Theorem 1.21 (triangle_vandermonde).

Lean statement: D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.triangle_vandermonde

Proof. Machine-checked in Lean as D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.triangle_vandermonde (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. Bojko Bakalov and Victor G. Kac (2004). Twisted Modules over Lattice Vertex Algebras. DOI: 10.1142/9789812702562_0001. URL: https://arxiv.org/abs/math/0402315v1.

Commentary.

The two ordered Hahn coefficients are subtracted before support or evaluation. All numerator and diagonal exponents are signed. The signed kernel identity and complete residue calculation include positive-power cancellation and zero or empty degree fibers. The original contextual coefficient API is reused after its separate visibility publication. The original AB coefficient-field carriers and the three consumed ABOuterTaylor algebra helpers are kept here under their original declaration namespaces, without the unconsumed AB residue or middle-proof chains.

Theorem 1.22 (map_complex_smul).

Lean statement: D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.map_complex_smul

Proof. Machine-checked in Lean as D5/S3/VertexAlgebra/NestedResidues/BinaryLaurentEvaluation.map_complex_smul (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. Bojko Bakalov and Victor G. Kac (2004). Twisted Modules over Lattice Vertex Algebras. DOI: 10.1142/9789812702562_0001. URL: https://arxiv.org/abs/math/0402315v1.

Commentary.

The two ordered Hahn coefficients are subtracted before support or evaluation. All numerator and diagonal exponents are signed. The signed kernel identity and complete residue calculation include positive-power cancellation and zero or empty degree fibers. The original contextual coefficient API is reused after its separate visibility publication. The original AB coefficient-field carriers and the three consumed ABOuterTaylor algebra helpers are kept here under their original declaration namespaces, without the unconsumed AB residue or middle-proof chains.

References